Coupling surface acoustic wave resonators to a Josephson ring modulator

ABSTRACT

A superconducting device that mixes surface acoustic waves and techniques for fabricating the same are provided. A superconducting device can comprise a first surface acoustic wave resonator comprising a first low-loss piezo-electric dielectric substrate. The superconducting device can also comprise a second surface acoustic wave resonator comprising a second low-loss piezo-electric dielectric substrate. Further, the superconducting device can comprise a Josephson ring modulator coupled to the first surface acoustic wave resonator and the second surface acoustic wave resonator. The Josephson ring modulator is a dispersive nonlinear three-wave mixing element.

BACKGROUND

In quantum circuits, a Josephson ring modulator is coupled to twosuperconducting microwave resonators and three-way mixing is performedbetween differential modes supported by the two superconductingmicrowave resonators and a non-resonant, common drive fed to theJosephson ring modulator. Due to coupling the Josephson ring modulatorto the two superconducting microwave resonators, the device is limitedin the choice of the frequency of differential modes, which can causeone or more problems. For example, coupling the Josephson ring modulatorto low-frequency, transmission-line resonators can have variousproblems, such as occupying a large area (e.g., a large footprint).Another problem is the relatively large linear inductance associatedwith the low resonance-frequency transmission-line compared to theinductance of the Josephson ring modulator. This can result in a veryreduced participation ratio which in turn requires, for its operation,very high external quality factors (Qs) for the resonators. However,high external Qs for the resonators is undesirable because it can giverise to very narrow dynamical bandwidths, which severely limit thedevice usability and practicality.

In addition, coupling the Josephson ring modulator to low-frequency,lumped-element resonators can require the use of large lumpedcapacitances and large lumped inductances. Large lumped capacitances andinductances are difficult to realize in practice. Large capacitances canhave considerable loss (lowering the internal Q of the device) and as aresult can cause a considerable portion of the quantum signal to belost. Large geometric inductances usually suffer from parasiticcapacitances which limit their utility. Large kinetic inductancesusually rely on unconventional thin superconductors which are difficultto fabricate and integrate.

SUMMARY

The following presents a summary to provide a basic understanding of oneor more embodiments of the invention. This summary is not intended toidentify key or critical elements, or delineate any scope of theparticular embodiments or any scope of the claims. Its sole purpose isto present concepts in a simplified form as a prelude to the moredetailed description that is presented later. In one or more embodimentsdescribed herein are devices, systems, methods, computer-implementedmethods, apparatuses, and/or computer program products that mix surfaceacoustic waves.

According to an embodiment, a superconducting device can comprise afirst surface acoustic wave resonator comprising a first low-losspiezo-electric dielectric substrate. The superconducting device can alsocomprise a second surface acoustic wave resonator comprising a secondlow-loss piezo-electric dielectric substrate. Further, thesuperconducting device can comprise a Josephson ring modulator coupledto the first surface acoustic wave resonator and the second surfaceacoustic wave resonator. The Josephson ring modulator can be adispersive nonlinear three-wave mixing element. An advantage of such asuperconducting device is that dissipationless, three-wave mixing andamplification can be performed between microwave frequencies of thefirst superconducting surface acoustic wave resonator and the secondsuperconducting surface acoustic wave resonator.

In some examples, the first surface acoustic wave resonator can comprisea first superconducting Bragg mirror and a second superconducting Braggmirror separated from the first superconducting Bragg mirror by a firstdistance. The second surface acoustic wave resonator can comprise athird superconducting Bragg mirror and a fourth superconducting Braggmirror separated from the third superconducting Bragg mirror by a seconddistance. The first distance and the second distance can be odd integermultiples of a half-wavelength supported by the first surface acousticwave resonator and the second surface acoustic wave resonator. Anadvantage of such a superconducting device is that the superconductingdevice can operate over a single, a few, or many modes of thesuperconducting surface acoustic wave resonators.

According to some implementations, the superconducting device can alsoadvantageously comprise a first external feedline coupled to the firstsurface acoustic wave resonator through a first interdigitatedcapacitance device. The first external feedline carries first inputsignals and first output signals of the first surface acoustic waveresonator. Further, the superconducting device can comprise a secondexternal feedline coupled to the second surface acoustic wave resonatorthrough a second interdigitated capacitance device. The second externalfeedline carries second input signals and second output signals of thesecond surface acoustic wave resonator. An advantage of such asuperconducting device is that frequencies of the first superconductingsurface acoustic wave resonator and the second superconducting surfaceacoustic wave resonator can be received, mixed, and amplified.

According to an embodiment, provided is a superconducting circuit thatcan comprise a Josephson ring modulator, a first surface acoustic waveresonator and a second surface acoustic wave resonator. The firstsurface acoustic wave resonator can be coupled via a firstsuperconducting wire to a first node of the Josephson ring modulator andvia a second superconducting wire to a second node of the Josephson ringmodulator. The first superconducting wire and the second superconductingwire can comprise a same length. The second surface acoustic waveresonator can be coupled via a third superconducting wire to a thirdnode of the Josephson ring modulator and via a fourth superconductingwire to a fourth node of the Josephson ring modulator. The thirdsuperconducting wire and the fourth superconducting wire can comprise asame length. The first surface acoustic wave resonator is spatially andspectrally separated from the second surface acoustic wave resonator. Anadvantage of such a superconducting circuit is that dissipationless,three-wave mixing and amplification can be facilitated between lowmicrowave frequencies of the first superconducting surface acoustic waveresonator and the second superconducting surface acoustic waveresonator.

In accordance with some implementations, the superconducting circuit cancomprise a first external feedline coupled to the first surface acousticwave resonator through a first interdigitated capacitance device. Thefirst external feedline can carry first input signals and first outputsignals of the first surface acoustic wave resonator. Thesuperconducting circuit can also comprise a second external feedlinecoupled to the second surface acoustic wave resonator through a secondinterdigitated capacitance device. The second external feedline cancarry second input signals and second output signals of the secondsurface acoustic wave resonator. An advantage of such a superconductingcircuit is that a first set of frequencies of the first superconductingsurface acoustic wave resonator and a second set of frequencies of thesecond superconducting surface acoustic wave resonator can be received,mixed, and amplified.

Another embodiment relates to a method that can comprise coupling afirst superconducting surface acoustic wave resonator to a Josephsonring modulator. The method can also comprise coupling a secondsuperconducting surface acoustic wave resonator to the Josephson ringmodulator. The Josephson ring modulator can comprise one or moreJosephson junctions arranged in a Wheatstone-bridge configuration.Further, the Josephson ring modulator can be a dispersive nonlinearthree-wave mixing element. An advantage of such a method is that asuperconducting device can be fabricated, which can performdissipationless, three-wave mixing between first microwave frequenciesof the first superconducting surface acoustic wave resonator and secondmicrowave frequencies of the second superconducting surface acousticwave resonator.

A further embodiment relates to a superconducting device that cancomprise a first superconducting surface acoustic wave resonatorcomprising a first interdigitated capacitance device positioned at afirst center of the first superconducting surface acoustic waveresonator. The first surface acoustic wave resonator can also comprise afirst superconducting Bragg mirror and a second superconducting Braggmirror separated from the first superconducting Bragg mirror by a firstdistance. The superconducting device can also comprise a secondsuperconducting surface acoustic wave resonator comprising a secondinterdigitated capacitance device positioned at a second center of thesecond superconducting surface acoustic wave resonator. The secondsuperconducting surface acoustic wave resonator can also comprise athird superconducting Bragg mirror and a fourth superconducting Braggmirror separated from the third superconducting Bragg mirror by a seconddistance. The first distance and the second distance are odd integermultiples of a half-wavelength supported by the first surface acousticwave resonator and the second surface acoustic wave resonator. Further,the superconducting device can comprise a Josephson ring modulatorcoupled to the first superconducting surface acoustic wave resonator andthe second superconducting surface acoustic wave resonator. A first setof opposite nodes of the Josephson ring modulator can be connected toopposite nodes of the first interdigitated capacitance device. A secondset of opposite nodes of the Josephson ring modulator can be connectedto opposite nodes of the second interdigitated capacitance device. Anadvantage of such a superconducting device is that dissipationless,three-wave mixing and amplification can be performed between microwavefrequencies of the first superconducting surface acoustic wave resonatorand microwave frequencies of the second superconducting surface acousticwave resonator while occupying a small space and through the use oflow-loss resonators.

Another embodiment relates to a superconducting device comprising afirst superconducting surface acoustic wave resonator comprising a firstsuperconducting Bragg mirror and a second superconducting Bragg mirrorseparated from the first superconducting Bragg mirror by a firstdistance. The superconducting device can also comprise a secondsuperconducting surface acoustic wave comprising a third superconductingBragg mirror and a fourth superconducting Bragg mirror separated fromthe third superconducting Bragg mirror by a second distance. The firstdistance and the second distance are odd integer multiples of ahalf-wavelength supported by the first surface acoustic wave resonatorand the second surface acoustic wave resonator. In addition, the secondsuperconducting surface acoustic wave resonator can be spatially andspectrally separated from the first superconducting surface acousticwave resonator. Further, the superconducting device can comprise aJosephson ring modulator comprising a first set of opposite nodes and asecond set of opposite nodes. The Josephson ring modulator can beconnected to the first superconducting surface acoustic wave resonatorvia the first set of opposite nodes and to the second superconductingsurface acoustic wave resonator via the second set of opposite nodes. Anadvantage of such a superconducting device is that dissipationless,three-wave mixing and amplification can be performed between microwavefrequencies of the first superconducting surface acoustic wave resonatorand microwave frequencies of the second superconducting surface acousticwave resonator while occupying a small space through the use of low-lossresonators.

DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example, non-limiting block diagram of a circuitin accordance with one or more embodiments described herein.

FIG. 2 illustrates an example, non-limiting block diagram of a circuitcomprising two superconducting surface acoustic wave resonators inaccordance with one or more embodiments described herein.

FIG. 3 illustrates an example, non-limiting, schematic of a circuit fora superconducting device that comprises surface acoustic wave resonatorscoupled to a Josephson ring modulator in accordance with one or moreembodiments described herein.

FIG. 4 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a device in accordance with one or more embodimentsdescribed herein.

FIG. 5 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a device comprising two superconducting surfaceacoustic wave resonators in accordance with one or more embodimentsdescribed herein.

FIG. 6 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a device comprising a pump drive port in accordancewith one or more embodiments described herein.

FIG. 7 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a device comprising external feedlines in accordancewith one or more embodiments described herein.

FIG. 8 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a superconducting quantum device in accordance withone or more embodiments described herein.

FIG. 9 illustrates a flow diagram of an example, non-limiting, methodfor fabrication of a superconducting quantum device comprising externalfeedlines in accordance with one or more embodiments described herein.

FIG. 10 illustrates a block diagram of an example, non-limitingoperating environment in which one or more embodiments described hereincan be facilitated.

DETAILED DESCRIPTION

The following detailed description is merely illustrative and is notintended to limit embodiments and/or application or uses of embodiments.Furthermore, there is no intention to be bound by any expressed orimplied information presented in the preceding Background or Summarysections, or in the Detailed Description section.

One or more embodiments are now described with reference to thedrawings, wherein like referenced numerals are used to refer to likeelements throughout. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea more thorough understanding of the one or more embodiments. It isevident, however, in various cases, that the one or more embodiments canbe practiced without these specific details.

As it relates to circuits, and more specifically quantum circuits, if aJosephson ring modulator (JRM) is coupled to two superconductingmicrowave resonators, there is a limitation with respect to the choiceof the differential modes that couple to the JRM. For example, a problemassociated with coupling the JRM to low-frequency, transmission-lineresonators is that a large area is occupied by the device. A solutionprovided by the superconducting device, the superconducting circuit, andthe methods discussed herein is that two superconducting surfaceacoustic wave resonators are utilized. The superconducting surfaceacoustic wave resonators are compact as compared to superconducting waveresonators and, therefore, a size of the superconducting device isreduced.

Another problem associated with prior art superconducting devices (e.g.,devices that utilize two superconducting microwave resonators) is thatthe prior art superconducting devices are limited to mixing frequenciesbetween 5 Gigahertz (GHz) and 15 GHz. The various superconductingdevices, circuits, and methods discussed herein provide a solution tothis problem through the utilization of superconducting surface acousticwave resonators that enable dissipationless, three-wave mixing andamplification between low microwave frequencies (e.g., about 0.1 GHz toabout 4 GHz). Operation at these low microwave frequencies is notavailable using transmission line resonators or using lumped-elements asprovided with prior art superconducting devices.

Given the above problems with prior art superconducting devices, thevarious aspects provided herein can be implemented to produce a solutionto one or more of these problems in the form of a superconductingdevice, superconducting circuit, and method of fabricating the same.Such systems, devices, circuits, methods, computer-implemented methods,and/or computer program products implementing such a superconductingdevice can have an advantage of reduced size and low-loss resonators, ascompared to conventional techniques.

According to some implementations, the device can function as aJosephson mixer for surface acoustic waves (phonons). Additionally, oralternatively, the device can function as a lossless frequency converterbetween two surface acoustic waves. Additionally, or alternatively, thedevice can function as a nondegenerate parametric Josephson amplifierfor surface acoustic waves. In additional or alternativeimplementations, the device can function as an entangler of two phononicmodes (e.g., generating entanglement between two phononic modes).

FIG. 1 illustrates an example, non-limiting block diagram of a circuit100 in accordance with one or more embodiments described herein. Thecircuit 100 can comprise a first superconducting surface acoustic wave(SAW) resonator (referred to as a first superconducting SAW resonator102), a second superconducting SAW resonator 104, and a Josephson ringmodulator (referred to as a JRM 106).

In a piece of quantum hardware, which includes the superconductingqubits space, a mechanism to implement gate operations or measurementson the quantum hardware is to generate microwave signals or receivemicrowave signals by the first superconducting SAW resonator 102 and/orthe second superconducting SAW resonator 104. As discussed herein,according to some implementations, the circuit 100 can operate as aJosephson mixer between surface acoustic waves (phonons). Further, thecircuit 100 can operate as a lossless frequency converter between twosurface acoustic waves. In some implementations, the circuit 100 canoperate as a nondegenerate parametric Josephson amplifier for surfaceacoustic waves. In additional and/or alternate implementations, thedevice can operate as an entangler of two phononic modes.

SAW resonators (e.g., the first superconducting SAW resonator 102, thesecond superconducting SAW resonator 104) are electro-mechanicalresonators for phonons, which can resonate at microwave frequencies ofaround 0.5 GHz to 5 GHz. Surface acoustic wave resonators (or surfaceacoustic wave filters) are used in many telecommunication applications(e.g., mobile phones). SAW resonators can also be useful in quantumcomputing applications and quantum circuits in the microwave domain, asdiscussed herein. Further, surface acoustic wave resonators can havehigh internal Quality (Q) factors, which can be in excess of 10⁵.Therefore, SAW resonators can have a very low loss. In addition, SAWresonators are very compact. For example, the surface acoustic resonancewavelengths are very short (e.g., less than 1 micro metre or <1 μm).

The first superconducting SAW resonator 102 can comprise a firstresonance frequency and the second superconducting SAW resonator 104 cancomprise a second resonance frequency. Further, the firstsuperconducting SAW resonator 102 and the second superconducting SAWresonator 104 can be implemented on respective low-loss piezo-electricdielectric substrates. The low-loss piezo-dielectric substrates cancomprise a material selected from a group of materials comprisingquartz, gallium arsenide, lithium niobite, and/or zinc oxide, or thelike.

The JRM 106 is a device that can be based on Josephson tunnel junctions.For example, the JRM 106 can comprise one or more Josephson junctionsarranged in a Wheatstone-bridge configuration. The one or more Josephsonjunctions can comprise a material selected from a group of materialscomprising aluminum and niobium. Further, the JRM 106 can performnon-degenerate mixing in the microwave regime, without losses. Accordingto some implementations, the JRM 106 can be a dispersive nonlinearthree-wave mixing element.

The JRM 106 can support two differential modes and two common modes (oneof which is at zero frequency, and, therefore, not applicable to the oneor more embodiments described herein). By coupling the JRM 106 to asuitable electromagnetic environment (which supports two differentialmicrowave modes), the circuit 100 can be used to perform various quantumprocessing operations such as lossless frequency conversion in themicrowave domain, parametric amplification at the quantum limit (e.g.,amplification of quantum signals in the microwave domain), and/orgeneration of two-mode squeezing.

The Josephson ring modulator (e.g., the JRM 106) can comprise one ormore Josephson junctions arranged in a Wheatstone-bridge configuration.The Josephson junctions are illustrated as a first Josephson junction108, a second Josephson junction 110, a third Josephson junction 112,and a fourth Josephson junction 114. The Josephson junctions (e.g., thefirst Josephson junction 108, the second Josephson junction 110, thethird Josephson junction 112, the fourth Josephson junction 114) can beformed in a loop. Further, the Josephson junctions can be utilized toperform the mixing as discussed herein.

The JRM 106 also can comprise four additional junctions (internal to theloop), which can be shunt junctions according to some implementations.These four additional junctions are labeled as a first internal junction116, a second internal junction 118, a third internal junction 120, anda fourth internal junction 122. The four internal junctions (e.g., thefirst internal junction 116, the second internal junction 118, the thirdinternal junction 120, and the fourth internal junction 122) canfacilitate tuning of the frequency of the circuit 100. The tunabilitycan be obtained with the application of external magnetic flux. In thisconfiguration, the four internal junctions, which are larger than thejunctions on the outer loop, can function as linear inductors shuntingthe outer Josephson junctions. By threading external flux through theinner loops, the total inductance of the JRM 106 can change, which canlead to a change in the resonance frequencies of the resonator coupledto the JRM 106.

In addition, the configuration of the JRM 106 defines points or nodeswhere the external junctions meet. Accordingly, there can be a firstnode 124 at the bottom of the JRM 106; a second node 126 at the rightside of the JRM 106; a third node 128 at the top of the JRM 106; and afourth node 130 at the left side of the JRM 106. It is noted that theterms bottom, right side, top, and left side are for purposes ofexplaining the disclosed aspects with respect to the figures and thedisclosed aspects are not limited to any particular plane or orientationof the JRM 106 and/or the circuit 100 and its associated circuitry.

The four nodes (e.g., the first node 124, the second node 126, the thirdnode 128, and the fourth node 130) can be utilized to define thedifferential mode and the common mode hosted by the circuit 100. Themodes can be orthogonal and do not overlap one another. Further, thenodes, as illustrated, can be physically orthogonal. For example, thefirst node 124 and the third node 128 are vertical to one another andthe second node 126 and the fourth node 130 are horizontal to oneanother.

The nodes can be utilized to couple the JRM 106 to the firstsuperconducting SAW resonator 102 and to the second superconducting SAWresonator 104. For example, a first set of opposite nodes (e.g., thefirst node 124 and the third node 128) can be chosen to operativelycouple the JRM 106 to the first superconducting SAW resonator 102. Thefirst node 124 can be coupled to the first superconducting SAW resonator102 via a first superconducting wire 132 (or first lead) and the thirdnode 128 can be coupled to the first superconducting SAW resonator 102via a second superconducting wire 134 (or second lead).

The second set of opposite nodes (e.g., the second node 126 and thefourth node 130) can be chosen to operatively couple the JRM 106 to thesecond superconducting SAW resonator 104. For example, the second node126 can be coupled to the second superconducting SAW resonator 104 via athird superconducting wire 136 (or third lead) and the fourth node 130can be coupled to the second superconducting SAW resonator 104 via afourth superconducting wire 138 (or fourth lead).

As illustrated, the first superconducting wire 132 and the secondsuperconducting wire 134 can be coupled to the first superconducting SAWresonator 102 at different locations of the first superconducting SAWresonator 102. Further, the third superconducting wire 136 and thefourth superconducting wire 138 can be coupled to the secondsuperconducting SAW resonator 104 at different locations of the secondsuperconducting SAW resonator 104. Further details related to thecoupling locations will be provided below with respect to FIG. 3.

The first superconducting SAW resonator 102, the second superconductingSAW resonator 104, and the JRM 106 are portions of afrequency-converter/mixer/amplifier/entangler device. The device canreceive external microwave photons or phonons at microwave frequenciesfrom other quantum devices connected to the SAW port (e.g., an idlerport) and/or the SAW port (e.g., a signal port) of the device.

The circuit 100, as well as other aspects discussed herein can beutilized in a device that facilitates manipulation of quantuminformation in accordance with one or more embodiments described herein.Aspects of devices (e.g., the circuit 100 and the like), systems,apparatuses, or processes explained in this disclosure can constitutemachine-executable component(s) embodied within machine(s), e.g.,embodied in one or more computer readable mediums (or media) associatedwith one or more machines. Such component(s), when executed by the oneor more machines, e.g., computer(s), computing device(s), virtualmachine(s), etc. can cause the machine(s) to perform the operationsdescribed.

In various embodiments, the device can be any type of component,machine, system, device, facility, apparatus, and/or instrument thatcomprises a processor and/or can be capable of effective and/oroperative communication with a wired and/or wireless network.Components, machines, apparatuses, systems, devices, facilities, and/orinstrumentalities that can comprise the device can include tabletcomputing devices, handheld devices, server class computing machinesand/or databases, laptop computers, notebook computers, desktopcomputers, cell phones, smart phones, consumer appliances and/orinstrumentation, industrial and/or commercial devices, hand-helddevices, digital assistants, multimedia Internet enabled phones,multimedia players, and the like.

In various embodiments, the device can be a quantum computing device orquantum computing system associated with technologies such as, but notlimited to, quantum circuit technologies, quantum processortechnologies, quantum computing technologies, artificial intelligencetechnologies, medicine and materials technologies, supply chain andlogistics technologies, financial services technologies, and/or otherdigital technologies. The circuit 100 can employ hardware and/orsoftware to solve problems that are highly technical in nature, that arenot abstract and that cannot be performed as a set of mental acts by ahuman. Further, in certain embodiments, some of the processes performedcan be performed by one or more specialized computers (e.g., one or morespecialized processing units, a specialized computer with a quantumcomputing component, etc.) to carry out defined tasks related to machinelearning.

The device and/or components of the device can be employed to solve newproblems that arise through advancements in technologies mentionedabove, computer architecture, and/or the like. One or more embodimentsof the device can provide technical improvements to quantum computingsystems, quantum circuit systems, quantum processor systems, artificialintelligence systems and/or other systems. One or more embodiments ofthe circuit 100 can also provide technical improvements to a quantumprocessor (e.g., a superconducting quantum processor) by improvingprocessing performance of the quantum processor, improving processingefficiency of the quantum processor, improving processingcharacteristics of the quantum processor, improving timingcharacteristics of the quantum processor, and/or improving powerefficiency of the quantum processor.

FIG. 2 illustrates an example, non-limiting block diagram of a circuit200 comprising two superconducting surface acoustic wave (SAW)resonators in accordance with one or more embodiments described herein.Repetitive description of like elements employed in other embodimentsdescribed herein is omitted for sake of brevity.

The first superconducting SAW resonator 102 can comprise a firstsuperconducting metallic/dielectric mirror (e.g., a first Bragg mirror202) and a second superconducting metallic/dielectric mirror (e.g., asecond Bragg mirror 204). The first Bragg mirror 202 can be separatedfrom the second Bragg mirror 204 by a distance that is an odd integermultiple of a half-wavelength supported by the first superconducting SAWresonator 102. The Bragg mirrors comprise respective periodic structuresof metallic fingers and dielectric gaps positioned at a defined distancefrom one another.

According to some implementations, the first superconducting SAWresonator 102 can be attached to (e.g., realized on) a low-losspiezo-electric dielectric substrate (not shown). The low-losspiezo-electric dielectric substrate can comprise a material selectedfrom a group of materials comprising one or more of quartz, galliumarsenide, lithium niobite, and zinc oxide, or a similar material.

Further, a first interdigitated capacitance device or first IDC device206 and a second IDC device 208 can be included in the firstsuperconducting SAW resonator 102. The first IDC device 206 can couplebetween the first superconducting SAW resonator 102 and the JRM 106. Thesecond IDC device 208 can couple between the first superconducting SAWresonator 102 and an external port (e.g., a signal port 210).

For example, the first IDC device 206 can be positioned at a center ofthe first superconducting SAW resonator 102. A first set of oppositenodes of the JRM 106 can be connected to opposite nodes of the first IDCdevice 206. For example, the first node 124 of the JRM 106 can beconnected to a first side of the first IDC device 206 (e.g., via thefirst superconducting wire 132). Further, the third node 128 of the JRM106 can be connected to a second side of the first IDC device 206 (e.g.,via the second superconducting wire 134).

The second superconducting SAW resonator 104 can comprise a firstsuperconducting metallic/dielectric mirror (e.g., illustrated as a thirdBragg mirror 212) and a second superconducting metallic/dielectricmirror (e.g., illustrated as a fourth Bragg mirror 214). The third Braggmirror 212 can be separated from the fourth Bragg mirror 214 by adistance that is an odd integer multiple of a half-wavelength supportedby the second superconducting SAW resonator 104. The Bragg mirrorscomprise respective periodic structures of metallic fingers anddielectric gaps positioned at a defined distance from one another.

According to some implementations, the second superconducting SAWresonator 104 can be attached to (e.g., realized on) a low-losspiezo-electric dielectric substrate (not shown). The low-losspiezo-electric dielectric substrate can comprise a material selectedfrom a group of materials comprising one or more of quartz, galliumarsenide, lithium niobite, and zinc oxide, or a similar material.

Further, the second superconducting SAW resonator 104 can comprise afirst interdigitated capacitance device (e.g., illustrated as a thirdIDC device 216) and a second interdigitated capacitance device (e.g.,illustrated as a fourth IDC device 218). The third IDC device 216 cancouple between the second superconducting SAW resonator 104 and the JRM106. The fourth IDC device 218 can couple between the secondsuperconducting SAW resonator 104 and an external port (e.g., an idlerport 220).

For example, the third IDC device 216 can be positioned at a center ofthe second superconducting SAW resonator 104. A second set of oppositenodes of the JRM 106 can be connected to opposite nodes of the third IDCdevice 216. For example, the second node 126 of the JRM 106 can beconnected to a first side of the third IDC device 216 (e.g., via thethird superconducting wire 136). Further, the fourth node 130 of the JRM106 can be connected to a second side of the third IDC device 216 (e.g.,via the fourth superconducting wire 138).

The circuit 100 can also comprise a first external feedline 222 coupledto the first superconducting SAW resonator 102 through the second IDCdevice 208. The first external feedline 222 can be connected to thesignal port 210 (e.g., a radio frequency (rf) source). The firstexternal feedline 222 can carry one or more input signals and one ormore output signals of the first superconducting SAW resonator 102.

A second external feedline 224 can be coupled to the secondsuperconducting SAW resonator 104 through the fourth IDC device 218. Thesecond external feedline 224 can be connected to the idler port 220. Thesecond external feedline 224 can carry one or more input signals and oneor more output signals of the second superconducting SAW resonator 104.

Further, the JRM 106 can be operatively connected to a pump port 226(e.g., via coupling to the first superconducting wire 132 and the secondsuperconducting wire 134 or other wires). The pump port 226 can beconnected to a microwave source. The pump port 226 can supply therequired energy for the operation of the circuit 100. For example, uponor after pump power is supplied from the pump port 226 to the JRM 106,the first superconducting SAW resonator 102 and the secondsuperconducting SAW resonator 104 can be electrically connected throughthe JRM 106. However, when power is not supplied through the pump port226 (e.g., the power supply is off), the first superconducting SAWresonator 102 and the second superconducting SAW resonator 104 can beelectrically isolated from one another.

For amplification, ideally there would be a microwave signal that ispropagating on the idler transmission line (e.g., the second externalfeedline 224) that is connected to the idler port 220. In an example,assume that the microwave signal is weak and it carries some quantuminformation that is of value. The information goes into the circuit 100and there is a pump tone that is fed to the device (e.g., via the pumpport 226) that can generate a parametric amplification between the idlermode and the signal mode supported by the first superconducting SAWresonator 102. In this example, an input signal is not needed at boththe signal port 210 and the idler port 220. Instead, a signal is onlyneeded on one port and quantum noise can enter through the other port.The deterministic signal carrying quantum information and the quantumnoise can be mixed by the device via the pump drive and amplified uponleaving the device. Thus, the signal that carries information can comeeither from the signal port 210, or the idler port 220, or can have twosignals carrying information entering both ports at substantially thesame time. For simplicity, assume the signal is entering the circuit 100through one port and the other port is only receiving quantum noise. Inthis case, through the interaction with the pump (e.g., the pump port226) and the JRM 106 three-wave mixing takes place between the commonmode (pump) and two differential modes (the idler and the signal). Ifthe pump frequency is the sum of the signal and idler resonancefrequencies, the device functions as a phase-preserving parametricamplifier operating near the quantum limit. The respective output signalexiting the signal port 210 and the idler port 220 can be an amplifiedsuperposition of the input signals entering both ports (e.g., the signalport 210 and the idler port 220).

According to some implementations, magnetic flux threading the JRM 106can be induced through the one or more external superconducting magneticcoils. For example, magnetic flux threading the JRM 106 can be inducedusing external superconducting magnetic coils attached to a devicepackage or using on-chip flux lines.

In further detail, FIG. 3 illustrates an example, non-limiting,schematic of a circuit 300 for a superconducting device that comprisessurface acoustic wave resonators coupled to a Josephson ring modulatorin accordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity.

It is noted that the Josephson junctions and the four internal junctionsof the JRM 106 are not labeled in FIG. 3 for purposes of simplicity.However, the element numbering of the junctions for purposes ofexplanation are the same as the labeling of FIGS. 1 and 2. In addition,the circuit 300 and its associated components can be implemented on asingle chip, according to some implementations.

As mentioned, the nodes of the JRM 106 can comprise a first set ofopposite nodes that can be oriented in a vertical direction to oneanother. For example, the first set of opposite nodes can comprise thefirst node 124 and the third node 128, which can operatively couple theJRM 106 to the first superconducting SAW resonator 102 (e.g., via thefirst superconducting wire 132 and the second superconducting wire 134).Further, the nodes of the JRM 106 can comprise a second set of oppositenodes, which can be oriented in a horizontal manner. For example, thesecond set of opposite nodes can comprise the second node 126 and thefourth node 130, which can operatively couple the JRM 106 to the secondsuperconducting SAW resonator 104 (e.g., via the third superconductingwire 136 and the fourth superconducting wire 138). It is noted thatalthough illustrated and described with respect to a horizontaldirection and/or a vertical direction, the disclosed aspects are notlimited to this orientation and other orientations can be utilized.

The first set of opposite nodes (e.g., the first node 124 and the thirdnode 128) can be coupled to opposite electrodes of the first IDC device206 of the first superconducting SAW resonator 102, creating a firstorthogonal mode. For example, the first node 124 of the JRM 106 can becoupled to a first electrode of the first IDC device 206, indicated at302 (e.g., via the first superconducting wire 132). Further, the thirdnode 128 of the JRM 106 can be coupled to a second electrode of thefirst IDC device 206, indicated at 304 (e.g., via the secondsuperconducting wire 134). The first IDC device 206 can be positioned ata center of the first superconducting SAW resonator 102.

The second set of opposite nodes (e.g., the second node 126 and thefourth node 130) can be can be coupled to opposite electrodes of thethird IDC device 216 of the second superconducting SAW resonator 104,creating a second orthogonal mode. For example, the second node 126 ofthe JRM 106 can be coupled to a first electrode of the third IDC device216, indicated at 306 (e.g., via the third superconducting wire 136).Further, the fourth node 130 of the JRM 106 can be coupled to a secondelectrode of the third IDC device 216, indicated at 308 (e.g., via thefourth superconducting wire 138). The third IDC device 216 can bepositioned at a center of the second superconducting SAW resonator 104.

As illustrated, the first superconducting SAW resonator 102 can comprisethe first IDC device 206, the second IDC device 208, and a set ofmetallic/dielectric mirrors (e.g., the first Bragg mirror 202 and thesecond Bragg mirror 204). The components of the first superconductingSAW resonator 102 (e.g., the first IDC device 206, the second IDC device208, the first Bragg mirror 202, the second Bragg mirror 204) can beimplemented on a piezo-electric substrate. For example, the piezoelectric substrate can comprise one or more of quartz, gallium arsenide,lithium niobite, zinc oxide, and/or similar materials.

In a similar manner, the second superconducting SAW resonator 104 cancomprise the third IDC device 216, the fourth IDC device 218, and a setof metallic/dielectric mirrors (e.g., the third Bragg mirror 212 and thefourth Bragg mirror 214). The components of the second superconductingSAW resonator 104 (e.g., the third IDC device 216, the fourth IDC device218, the third Bragg mirror 212, the fourth Bragg mirror 214) can beimplemented on a piezo-electric substrate. For example, the piezoelectric substrate can comprise one or more of quartz, gallium arsenide,lithium niobite, zinc oxide, and/or similar materials.

Different ports can be utilized to access the first superconducting SAWresonator 102 and the second superconducting SAW resonator 104. Forexample, the signal port 210 can be utilized to access the firstsuperconducting SAW resonator 102 and the idler port 220 can be utilizedto access the second superconducting SAW resonator 104.

The signal port 210 can be utilized to carry input signals and outputsignals. Therefore, in order to measure output signals from the firstsuperconducting SAW resonator 102, an IDC (e.g., the second IDC device208) can be placed between the first Bragg mirror 202 and the secondBragg mirror 204. One set of IDC fingers that are connected together arelocated at an rf-voltage anti-node (maximum/minimum) of the supportedphononic mode. Therefore, the spacing between the fingers can bedetermined by the wavelength supported by the first superconducting SAWresonator 102.

A distance between the centers of two consecutive fingers of the IDCs(e.g., the first IDC device 206 and the second IDC device 208) can begenerally expressed as λ_(a)/2. The respective two sets of fingers ofthe IDCs can have opposite polarity according to an implementation.Further, the first Bragg mirror 202 and the second Bragg mirror 204 canbe separated from one other, as indicated by line 312, by a distancethat is an odd integer multiple of half-wavelength supported by thefirst superconducting SAW resonator 102. The defined distance can beexpressed as L_(a), wherein L_(a) is an odd-integer multiple of λ_(a)/2.

The idler port 220 can be utilized to carry input signals and outputsignals. Therefore, in order to measure output signals from the secondsuperconducting SAW resonator 104, an IDC (e.g., the fourth IDC device218) can be placed between the third Bragg mirror 212 and the fourthBragg mirror 214. One set of IDC fingers that are connected together arelocated at an rf-voltage anti-node (maximum/minimum) of the supportedphononic mode. Therefore, the spacing between the fingers can bedetermined by the wavelength supported by the second superconducting SAWresonator 104.

A distance between the centers of two consecutive fingers of the IDCs(e.g., the third IDC device 216 and the fourth IDC device 218) can begenerally expressed as λ_(b)/2. The respective two sets of fingers ofthe IDCs can have opposite polarity according to an implementation.Further, the third Bragg mirror 212 and the fourth Bragg mirror 214 canbe separated from one other, as indicated by line 314, by a distancethat is an odd integer multiple of half-wavelength supported by thesecond superconducting SAW resonator 104. The defined distance can beexpressed as L_(b), wherein L_(b) is an odd-integer multiple of λ_(b)/2.Where λ_(b)<λ_(a).

A microwave tone is characterized by a wave that has a maximum amplitudeand a minimum amplitude. The minimum amplitude should couple to onefinger of the first IDC device 206 (e.g., indicated at 302 or 304) andthe maximum amplitude should couple to the other finger, (e.g.,indicated at 304 or 302) where the two fingers are connected to oppositenodes of the JRM 106 (e.g., the first node 124 and the third node 128).Therefore, the distance λ_(a)/2 can be selected to facilitate themaximum on the first finger and the minimum on the other finger.

In a similar manner, the minimum amplitude should couple to one fingerof the third IDC device 216 (e.g., indicated at 306 or 308) and themaximum amplitude should couple to the other finger (e.g., indicated at308 or 306) where the two fingers are connected to opposite nodes of theJRM 106 (e.g., the second node 126 and the fourth node 130). Therefore,the distance λ_(b)/2 can be selected to facilitate the maximum on thefirst finger and the minimum on the other finger.

Further, for purposes of explanation, the maximum amplitude has a plussign (or a positive value) and the minimum amplitude has a minus sign(or a negative value). Therefore, the two opposite nodes of the JRM 106can be excited by the positive (on the first finger) and the negativerf-voltages (on the second finger). These signals can alternate withtime. However, they should be opposite to one another at any given time.When the polarity is different, it can be referred to as a differentialmode (where differential means opposite sign). Accordingly, a firstdifferential mode of the JRM 106 is supported by the firstsuperconducting SAW resonator 102 and a second differential mode of theJRM 106 is supported by the second superconducting SAW resonator 104.

Further, in order to perform the mixing, or the amplification, microwaveenergy is supplied for device operation. The energy source for themixing and/or amplification is supplied through the pump port 226. Thepump port 226 can provide a microwave signal, which can be a strong,coherent, non-resonant microwave tone that can supply energy for thecircuit 100 to operate. According to some implementations, the microwavesignal supplied by the pump port 226 can comprise a frequency thatsatisfies a defined equation determined based on the energy conservationof the three-wave mixing occurring in the circuit 100.

In an example of amplification performed by the device, a first signalf_(a) which lies within the bandwidth of the first superconducting SAWresonator 102 and a second signal f_(b) which lies within the bandwidthof the second superconducting SAW resonator 104. Further, the frequencyof the second signal can be larger than the frequency of the firstsignal (f_(b)>f_(a)). To amplify both signals, the frequency of the pumptone fed through the pump port 226 should be the sum of the first signaland the second signal (e.g., f_(a)+f_(b)). The energy of theelectromagnetic signal is proportional to its frequency. By taking thepump (e.g., the pump port 226) frequency to be the sum, if the pumpinteracts with the dispersive nonlinear medium (e.g., the JRM 106), adownconversion process can occur where the energetic photons of the pumpsplit into a first set of phonons at f_(a) and a second set of phononsat f_(b). If the frequency is the sum, then the photons can split inthis manner. For example, the photons can split into two halves: a firsthalf (e.g., the first set of phonons) at the lower frequency f_(a) and asecond half (e.g., the second set of phonons) at the higher frequencyf_(b). Therefore, amplification can occur because the pump exchangesenergy with the signal mode and idler mode and through this exchangeentangled phonons are generated in both modes. In this case, the pumpfrequency should be equal to the difference between f_(a) and f_(b).Here f_(b) is larger, so the equation can be f_(b) minus f_(a).

As illustrated the gaps of the first IDC device 206 and the second IDCdevice 208 are larger (e.g., there is more distance between the fingers)than the gaps (or distance) of the third IDC device 216 and the fourthIDC device 218. The frequency f_(a) of the first superconducting SAWresonator 102 is lower than the frequency f_(b) of the secondsuperconducting SAW resonator 104. There is a one to one mapping betweenthe frequency and the wavelength. The frequencies are linked through thespeed of light or the speed of sound through the surface. If thewavelength (λ) times the frequency f is a constant, it is equal toeither the speed of light or the speed of sound in the medium. Since theproduct is fixed, if one is increased, the other one will decrease andvice versa. Thus, if the frequency is lowered, the correspondingwavelength will increase, and vice versa.

According to an implementation, in the mixing process a phonon in thefirst SAW resonator at the signal frequency can be upconverted into aphonon in the second SAW resonator at the idler frequency. According toanother implementation, the phonon in the second SAW resonator at theidler frequency can be downconverted to a phonon in the first SAWresonator at the signal frequency. The energy exchange is enabled by thepump drive (e.g., fed through the pump port 226). Accordingly, either apump photon is absorbed or a pump phonon is emitted to facilitate theprocess.

If there is no pump signal applied to the pump port 226, the firstsuperconducting SAW resonator 102 and the second superconducting SAWresonator 104 are separated (e.g., isolated from one another) andinformation exchange or information communications between the firstsuperconducting SAW resonator 102 and the second superconducting SAWresonator 104 does not occur. Upon or after a pump signal is applied tothe pump port 226, it excites the common mode of the JRM 106, asillustrated in FIG. 3, the first superconducting SAW resonator 102 andthe second superconducting SAW resonator 104 interact and information isexchanged.

According to some implementations, the pump drive is fed through thesigma port 318 of a 180-degree hybrid 316, which is capacitively coupledto opposite nodes of the JRM 106, which in turn excites a common-mode ofthe JRM 106. According to some implementations, the 180-degree hybrid316 operates as a power splitter.

By way of explanation and not limitation, a 180-degree hybrid is apassive microwave component that comprises four ports. A first port isreferred to as a sum port (e.g., the sigma port 318). If a signal isinput to the sigma port 318, the signal splits equally between two otherports (e.g., a second port 320 and a third port 322). The signals thatare output from the second port 320 and the third port 322 can have thesame phase. Thus, the first port is referred to as the sigma port 318because the phases of the split signals are equal. The pump drive (e.g.,the pump port 226) can be fed through the sigma port 318 of the180-degree hybrid 316.

A fourth port can be referred to as a delta port 324 (or a differenceport). If a signal is injected through the delta port 324 of the180-degree hybrid (which, in FIG. 3, is terminated with 50 ohms), thehybrid would split the signal into two signals, coming out of the twoports (e.g., the second port 320 and the third port 322), but the splitsignals have a 180-degree phase difference. For example, if a firstsignal has a maximum value at one port (e.g., the second port 320), thesecond signal at the other port (e.g., the third port 322) has a minimumvalue.

Also illustrated are a first lead 326 coming out of the second port 320and a second lead 328 coming out of the third port 322. The signals thatare output at the second port 320 and the third port 322 are half of thepump signal and have the same phase, as discussed above. The signalsencounter small coupling capacitors (e.g., a first coupling capacitor330 and a second coupling capacitor 332) that can be coupled to twoopposite nodes of the JRM 106. According to some implementations, thefirst coupling capacitor 330 and the second coupling capacitor 332 canbe respective capacitors chosen from a group of capacitors comprising agap capacitor, an interdigitated capacitor, and a plate capacitor. As itrelates to plate capacitance, the dielectric material should have verylow-loss at the level of single microwave photons.

The first coupling capacitor 330 can be coupled to the first node 124 ofthe JRM 106 (through the first IDC device 206) and the second couplingcapacitor 332 can be coupled to the third node 128 of the JRM 106. Infurther detail, the first lead 326 and the second lead 328 can couple totwo different sets of fingers of the first IDC device 206 (illustratedat the first contact point at the second electrode 304 and a thirdcontact point 334), that couple to two opposite nodes of the JRM 106.This connection enables exciting the common mode of the JRM 106 wherethe two opposite nodes of the JRM 106 are excited, not with oppositerf-voltage signs, but with equal signs. For example, the two oppositenodes can be excited with a positive-positive signal or anegative-negative signal.

The first lead 326 and the second lead 328 can be connectingsuperconducting wires that should be equal in length (e.g., phasematched) between the ports (e.g., the second port 320 and the third port322) of the 180 degree hybrid and the coupling capacitors (e.g., thefirst coupling capacitor 330 and the second coupling capacitor 332,respectively). Similarly, the first superconducting wire 132 and thesecond superconducting wire 134 pair, and the third superconducting wire136 and the fourth superconducting wire 138 pair, can be connectingsuperconducting wires that should be equal in length (e.g., phasematched) between the opposite nodes of the JRM 106 and the electrodes ofthe IDCs (e.g., the first IDC device 206, the third IDC device 216).Further, the connecting superconducting wires should be as short aspossible and wide (e.g., have small series inductance).

The following provides further technical comments for an understandingof the various aspects disclosed herein. The speed of sound in thevarious piezoelectric substrates can be slower than the speed of lightby several orders of magnitude (e.g., approximately five orders ofmagnitude, for example, 10⁵).

The effective length of the first superconducting SAW resonator 102 canbe slightly larger than L_(a). Further, the effective length of thesecond superconducting SAW resonator 104 can be slightly larger thanL_(b). The lengths are slightly larger than L_(a) and L_(b) because thereflection off the Bragg mirrors does not happen on the mirror edges butwithin a certain penetration depth inside the Bragg mirrors.

The effective length (L_(eff)) of the first superconducting SAWresonator 102 and/or the second superconducting SAW resonator 104 andthe speed of sound in the piezoelectric substrate (v_(s)) can determinethe cavity free spectral range (FSR):

$V_{FSR} = {\frac{v_{s}}{2L_{eff}}.}$The SAW resonators can be similar to photonic cavities that supportmultimodes (resonances). The cavity free spectral range parameter candetermine the frequency spacing between the multimodes supported by thefirst superconducting SAW resonator 102 and/or the secondsuperconducting SAW resonator 104.

The larger the spacing between the Bragg mirrors, the larger L_(eff) is,and as a result the smaller the frequency separation between the SAWresonator modes. The Bragg mirrors can operate as reflective mirrorswithin a certain bandwidth. Modes that fall beyond their bandwidth arenot supported by the SAW resonator because their phononic modes are notconfined.

Depending on the V_(FSR) and the bandwidth of the Bragg mirrors, thecircuit 100 can operate over a single, a few, or many modes of the SAWresonator. It is noted that not all the modes supported by the SAWresonator would strongly couple to the JRM. Three-wave mixing operationsin the circuit 100 can take place with phononic modes that couplestrongly to the JRM. Modes couple strongly to the JRM when theiranti-nodes align with the IDC fingers coupled to the JRM.

FIG. 4 illustrates a flow diagram of an example, non-limiting, method400 for fabrication of a device in accordance with one or moreembodiments described herein. Repetitive description of like elementsemployed in other embodiments described herein is omitted for sake ofbrevity.

At 402 of the method 400, a first surface acoustic wave resonator (e.g.,the first superconducting SAW resonator 102) can be coupled to aJosephson ring modulator (e.g., the JRM 106). For example, the firstsurface acoustic wave resonator can be coupled to a first set ofopposite nodes (e.g., the first node 124 and the third node 128) of theJosephson ring modulator.

The method 400 can also include, at 404, coupling a secondsuperconducting surface acoustic wave resonator (e.g., the secondsuperconducting SAW resonator 104) to the Josephson ring modulator. Thesecond superconducting surface acoustic wave resonator can be coupled toa first set of opposite nodes (e.g., the second node 126 and the fourthnode 130) of the Josephson ring modulator.

The Josephson ring modulator can comprise one or more Josephsonjunctions (e.g., the first Josephson junction 108, the second Josephsonjunction 110, the third Josephson junction 112, the fourth Josephsonjunction 114) arranged in a Wheatstone-bridge configuration. The one ormore Josephson junctions can comprise a first material selected from afirst group of materials comprising aluminum and niobium. Further, theJosephson ring modulator can be a dispersive nonlinear three-wave mixingelement.

FIG. 5 illustrates a flow diagram of an example, non-limiting, method500 for fabrication of a device comprising two superconducting surfaceacoustic wave resonators in accordance with one or more embodimentsdescribed herein. Repetitive description of like elements employed inother embodiments described herein is omitted for sake of brevity.

At 502 the method 500 can comprise forming a first superconductingsurface acoustic wave resonator (e.g., the first superconducting SAWresonator 102) comprising positioning a first interdigitated capacitancedevice (e.g., the first IDC device 206) at a first center of the firstsuperconducting surface acoustic wave resonator.

Further, at 504 the method can comprise forming a second superconductingsurface acoustic wave resonator (e.g., the second superconducting SAWresonator 104) comprising positioning a second interdigitatedcapacitance device (e.g., the third IDC device 216) at a second centerof the second superconducting surface acoustic wave resonator.

At 506 the method 500 can comprise connecting a first set of oppositenodes (e.g., the first node 124 and the third node 128) of a Josephsonring modulator (e.g., the JRM 106) to opposite nodes (e.g., the firstelectrode 302 and the second electrode 304) of the first interdigitatedcapacitance device.

In addition, at 508 the method 500 can comprise connecting a second setof opposite nodes (e.g., the second node 126 and the fourth node 130) ofthe Josephson ring modulator to opposite nodes (e.g., the thirdelectrode 306 and the fourth electrode 308) of the second interdigitatedcapacitance device.

FIG. 6 illustrates a flow diagram of an example, non-limiting, method600 for fabrication of a device comprising a pump drive port inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity.

The method 600 starts at 602, when a first surface acoustic waveresonator (e.g., the first superconducting SAW resonator 102) can becoupled to a Josephson ring modulator (e.g., the JRM 106). Further, at604, a second superconducting surface acoustic wave resonator (e.g., thesecond superconducting SAW resonator 104) can be coupled to theJosephson ring modulator.

Further, at 606, a first coupling capacitor (e.g., the first couplingcapacitor 330) can be coupled to a first port (e.g., the second port320) of a pump (e.g., the pump port 226) via a first superconductingwire (e.g., the first lead 326). In addition, at 608 the method cancomprise connecting a second coupling capacitor (e.g., the secondcoupling capacitor 332) to a second port (e.g., the third port 322) ofthe pump via a second superconducting wire. According to someimplementations, the first superconducting wire and the secondsuperconducting wire can be phase matched.

FIG. 7 illustrates a flow diagram of an example, non-limiting, method700 for fabrication of a device comprising external feedlines inaccordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity.

The method 700 starts, at 702, and a first superconducting surfaceacoustic wave resonator (e.g., the first superconducting SAW resonator102) can be coupled to a Josephson ring modulator (e.g., the JRM 106).The first superconducting surface acoustic wave resonator can berealized on a low-loss piezo-electric dielectric substrate. For example,the low-loss piezo-electric dielectric substrate can comprise one ormore materials selected from a group of materials comprising one or moreof quartz, gallium arsenide, lithium niobite, and zinc oxide.

Further, at 704, a second superconducting surface acoustic waveresonator (e.g., the second superconducting SAW resonator 104) can becoupled to the Josephson ring modulator. The second superconductingsurface acoustic wave resonator can be realized on a low-losspiezo-electric dielectric substrate. For example, the low-losspiezo-electric dielectric substrate can comprise one or more materialsselected from a group of materials comprising one or more of quartz,gallium arsenide, lithium niobite, and zinc oxide.

At 706 of the method 700, a first external feedline (e.g., the firstexternal feedline 222) can be coupled to the first superconductingsurface acoustic wave resonator through a first interdigitatedcapacitance device (e.g., the second IDC device 208). The first externalfeedline can carry first input signals and first output signals of thefirst superconducting surface acoustic wave resonator.

At 708, a second external feedline (e.g., the second external feedline224) can be coupled to the second superconducting surface acoustic waveresonator through a second interdigitated capacitance device (e.g., thefourth IDC device 218). The second external feedline can carry secondinput signals and second output signals of the second superconductingsurface acoustic wave resonator.

FIG. 8 illustrates a flow diagram of an example, non-limiting, method800 for fabrication of a superconducting quantum device in accordancewith one or more embodiments described herein. Repetitive description oflike elements employed in other embodiments described herein is omittedfor sake of brevity.

A first superconducting surface acoustic wave resonator (e.g., the firstsuperconducting SAW resonator 102) can be formed at 802 of the method800. The first superconducting surface acoustic wave resonator cancomprise a first interdigitated capacitance device (e.g., the first IDCdevice 206) positioned at a first center of the first superconductingsurface acoustic wave resonator.

At 804, a second superconducting surface acoustic wave resonator (e.g.,the second superconducting SAW resonator 104) can be formed. The secondsuperconducting surface acoustic wave resonator can comprise a secondinterdigitated capacitance device (e.g., the third IDC device 216)positioned at a second center of the second superconducting surfaceacoustic wave resonator.

Further, at 806, a Josephson ring modulator (e.g., the JRM 106) can becoupled to the first superconducting surface acoustic wave resonator andthe second superconducting surface acoustic wave resonator. A first setof opposite nodes (e.g., the first node 124 and the third node 128) ofthe Josephson ring modulator can be connected to opposite nodes of thefirst interdigitated capacitance device. A second set of opposite nodes(e.g., the second node 126 and the fourth node 130) of the Josephsonring modulator can be connected to opposite nodes of the secondinterdigitated capacitance device.

FIG. 9 illustrates a flow diagram of an example, non-limiting, method900 for fabrication of a superconducting quantum device comprisingexternal feedlines in accordance with one or more embodiments describedherein. Repetitive description of like elements employed in otherembodiments described herein is omitted for sake of brevity.

At 902 of the method 900, a first surface acoustic wave resonator (e.g.,the first superconducting SAW resonator 102) comprising a first low-losspiezo-electric dielectric substrate can be formed. Forming the firstsurface acoustic wave resonator can comprise, at 904, separating a firstsuperconducting Bragg mirror (e.g., the first Bragg mirror 202) from asecond superconducting Bragg mirror (e.g., the second Bragg mirror 204)by a first distance.

At 906, a first interdigitated capacitance device (e.g., the first IDCdevice 206) can be positioned at a first center of the first surfaceacoustic wave resonator. A first set of opposite nodes (e.g., the firstnode 124 and the third node 128) of the Josephson ring modulator can beconnected to opposite nodes (e.g., the first electrode 302 and thesecond electrode 304) of the first interdigitated capacitance device.

A second surface acoustic wave resonator (e.g., the secondsuperconducting SAW resonator 104) comprising a second low-losspiezo-electric dielectric substrate can be formed at 908. The firstsurface acoustic wave resonator can be spatially and spectrallyseparated from the second surface acoustic wave resonator. Forming thesecond surface acoustic wave resonator can comprise, at 910, separatinga third superconducting Bragg mirror (e.g., the third Bragg mirror 212)from a fourth superconducting Bragg mirror (e.g., the fourth Braggmirror 214) by a second distance.

At 912, a second interdigitated capacitance device (e.g., the third IDCdevice 216) can be positioned at a second center of the second surfaceacoustic wave resonator. A second set of opposite nodes (e.g., thesecond node 126 and the fourth node 130) of the Josephson ring modulatorcan be connected to opposite nodes (e.g., the third electrode 306 andthe fourth electrode 308) of the second interdigitated capacitancedevice.

The first low-loss piezo-electric dielectric substrate and the secondlow-loss piezo-electric dielectric substrate can comprise a materialselected from a group of materials comprising of quartz, galliumarsenide, lithium niobite, and zinc oxide.

At 914, a pump port (e.g., the pump port 226) can be coupled to theJosephson ring modulator. A pump drive is injected to the Josephson ringmodulator through the pump port. In an example, a first couplingcapacitor can be connected via a first superconducting wire to a firstport of the pump port (e.g., a first external port). Further, a secondcoupling capacitor can be connected via a second superconducting wire toa second port of the pump (e.g., a second external port). The firstsuperconducting wire and the second superconducting wire can be phasematched. For example, the first coupling capacitor can be connected to afirst port of a pump via a first superconducting wire comprising a firstwire length and the second coupling capacitor can be connected to asecond port of the pump via a second superconducting wire comprising asecond wire length. The first wire length and the second wire length canbe a same wire length.

For simplicity of explanation, the methodologies and/orcomputer-implemented methodologies are depicted and described as aseries of acts. It is to be understood and appreciated that the subjectinnovation is not limited by the acts illustrated and/or by the order ofacts, for example acts can occur in various orders and/or concurrently,and with other acts not presented and described herein. Furthermore, notall illustrated acts can be required to implement thecomputer-implemented methodologies in accordance with the disclosedsubject matter. In addition, those skilled in the art will understandand appreciate that the computer-implemented methodologies couldalternatively be represented as a series of interrelated states via astate diagram or events. Additionally, it should be further appreciatedthat the computer-implemented methodologies disclosed hereinafter andthroughout this specification are capable of being stored on an articleof manufacture to facilitate transporting and transferring suchcomputer-implemented methodologies to computers. The term article ofmanufacture, as used herein, is intended to encompass a computer programaccessible from any computer-readable device or storage media.

In order to provide a context for the various aspects of the disclosedsubject matter, FIG. 10 as well as the following discussion are intendedto provide a general description of a suitable environment in which thevarious aspects of the disclosed subject matter can be implemented. FIG.10 illustrates a block diagram of an example, non-limiting operatingenvironment in which one or more embodiments described herein can befacilitated. Repetitive description of like elements employed in otherembodiments described herein is omitted for sake of brevity. Withreference to FIG. 10, a suitable operating environment 1000 forimplementing various aspects of this disclosure can also include acomputer 1012. The computer 1012 can also include a processing unit1014, a system memory 1016, and a system bus 1018. The system bus 1018couples system components including, but not limited to, the systemmemory 1016 to the processing unit 1014. The processing unit 1014 can beany of various available processors. Dual microprocessors and othermultiprocessor architectures also can be employed as the processing unit1014. The system bus 1018 can be any of several types of busstructure(s) including the memory bus or memory controller, a peripheralbus or external bus, and/or a local bus using any variety of availablebus architectures including, but not limited to, Industrial StandardArchitecture (ISA), Micro-Channel Architecture (MSA), Extended ISA(EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB),Peripheral Component Interconnect (PCI), Card Bus, Universal Serial Bus(USB), Advanced Graphics Port (AGP), Firewire (IEEE 1394), and SmallComputer Systems Interface (SCSI). The system memory 1016 can alsoinclude volatile memory 1020 and nonvolatile memory 1022. The basicinput/output system (BIOS), containing the basic routines to transferinformation between elements within the computer 1012, such as duringstart-up, is stored in nonvolatile memory 1022. By way of illustration,and not limitation, nonvolatile memory 1022 can include read only memory(ROM), programmable ROM (PROM), electrically programmable ROM (EPROM),electrically erasable programmable ROM (EEPROM), flash memory, ornonvolatile random access memory (RAM) (e.g., ferroelectric RAM(FeRAM)). Volatile memory 1020 can also include random access memory(RAM), which acts as external cache memory. By way of illustration andnot limitation, RAM is available in many forms such as static RAM(SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rateSDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM),direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), andRambus dynamic RAM.

Computer 1012 can also include removable/non-removable,volatile/nonvolatile computer storage media. FIG. 10 illustrates, forexample, a disk storage 1024. Disk storage 1024 can also include, but isnot limited to, devices like a magnetic disk drive, floppy disk drive,tape drive, Jaz drive, Zip drive, LS-100 drive, flash memory card, ormemory stick. The disk storage 1024 also can include storage mediaseparately or in combination with other storage media including, but notlimited to, an optical disk drive such as a compact disk ROM device(CD-ROM), CD recordable drive (CD-R Drive), CD rewritable drive (CD-RWDrive) or a digital versatile disk ROM drive (DVD-ROM). To facilitateconnection of the disk storage 1024 to the system bus 1018, a removableor non-removable interface is typically used, such as interface 1026.FIG. 10 also depicts software that acts as an intermediary between usersand the basic computer resources described in the suitable operatingenvironment 1000. Such software can also include, for example, anoperating system 1028. Operating system 1028, which can be stored ondisk storage 1024, acts to control and allocate resources of thecomputer 1012. System applications 1030 take advantage of the managementof resources by operating system 1028 through program modules 1032 andprogram data 1034, e.g., stored either in system memory 1016 or on diskstorage 1024. It is to be appreciated that this disclosure can beimplemented with various operating systems or combinations of operatingsystems. A user enters commands or information into the computer 1012through input device(s) 1036. Input devices 1036 include, but are notlimited to, a pointing device such as a mouse, trackball, stylus, touchpad, keyboard, microphone, joystick, game pad, satellite dish, scanner,TV tuner card, digital camera, digital video camera, web camera, and thelike. These and other input devices connect to the processing unit 1014through the system bus 1018 via interface port(s) 1038. Interfaceport(s) 1038 include, for example, a serial port, a parallel port, agame port, and a universal serial bus (USB). Output device(s) 1040 usesome of the same type of ports as input device(s) 1036. Thus, forexample, a USB port can be used to provide input to computer 1012, andto output information from computer 1012 to an output device 1040.Output adapter 1042 is provided to illustrate that there are some outputdevices 1040 like monitors, speakers, and printers, among other outputdevices 1040, which require special adapters. The output adapters 1042include, by way of illustration and not limitation, video and soundcards that provide a method of connection between the output device 1040and the system bus 1018. It should be noted that other devices and/orsystems of devices provide both input and output capabilities such asremote computer(s) 1044.

Computer 1012 can operate in a networked environment using logicalconnections to one or more remote computers, such as remote computer(s)1044. The remote computer(s) 1044 can be a computer, a server, a router,a network PC, a workstation, a microprocessor based appliance, a peerdevice or other common network node and the like, and typically can alsoinclude many or all of the elements described relative to computer 1012.For purposes of brevity, only a memory storage device 1046 isillustrated with remote computer(s) 1044. Remote computer(s) 1044 islogically connected to computer 1012 through a network interface 1048and then physically connected via communication connection 1050. Networkinterface 1048 encompasses wire and/or wireless communication networkssuch as local-area networks (LAN), wide-area networks (WAN), cellularnetworks, etc. LAN technologies include Fiber Distributed Data Interface(FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ringand the like. WAN technologies include, but are not limited to,point-to-point links, circuit switching networks like IntegratedServices Digital Networks (ISDN) and variations thereon, packetswitching networks, and Digital Subscriber Lines (DSL). Communicationconnection(s) 1050 refers to the hardware/software employed to connectthe network interface 1048 to the system bus 1018. While communicationconnection 1050 is shown for illustrative clarity inside computer 1012,it can also be external to computer 1012. The hardware/software forconnection to the network interface 1048 can also include, for exemplarypurposes only, internal and external technologies such as, modemsincluding regular telephone grade modems, cable modems and DSL modems,ISDN adapters, and Ethernet cards.

The present invention may be a system, a method, an apparatus and/or acomputer program product at any possible technical detail level ofintegration. The computer program product can include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention. The computer readable storage medium can be atangible device that can retain and store instructions for use by aninstruction execution device. The computer readable storage medium canbe, for example, but is not limited to, an electronic storage device, amagnetic storage device, an optical storage device, an electromagneticstorage device, a semiconductor storage device, or any suitablecombination of the foregoing. A non-exhaustive list of more specificexamples of the computer readable storage medium can also include thefollowing: a portable computer diskette, a hard disk, a random accessmemory (RAM), a read-only memory (ROM), an erasable programmableread-only memory (EPROM or Flash memory), a static random access memory(SRAM), a portable compact disc read-only memory (CD-ROM), a digitalversatile disk (DVD), a memory stick, a floppy disk, a mechanicallyencoded device such as punch-cards or raised structures in a groovehaving instructions recorded thereon, and any suitable combination ofthe foregoing. A computer readable storage medium, as used herein, isnot to be construed as being transitory signals per se, such as radiowaves or other freely propagating electromagnetic waves, electromagneticwaves propagating through a waveguide or other transmission media (e.g.,light pulses passing through a fiber-optic cable), or electrical signalstransmitted through a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network can comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device. Computer readable programinstructions for carrying out operations of the present invention can beassembler instructions, instruction-set-architecture (ISA) instructions,machine instructions, machine dependent instructions, microcode,firmware instructions, state-setting data, configuration data forintegrated circuitry, or either source code or object code written inany combination of one or more programming languages, including anobject oriented programming language such as Smalltalk, C++, or thelike, and procedural programming languages, such as the “C” programminglanguage or similar programming languages. The computer readable programinstructions can execute entirely on the user's computer, partly on theuser's computer, as a stand-alone software package, partly on the user'scomputer and partly on a remote computer or entirely on the remotecomputer or server. In the latter scenario, the remote computer can beconnected to the user's computer through any type of network, includinga local area network (LAN) or a wide area network (WAN), or theconnection can be made to an external computer (for example, through theInternet using an Internet Service Provider). In some embodiments,electronic circuitry including, for example, programmable logiccircuitry, field-programmable gate arrays (FPGA), or programmable logicarrays (PLA) can execute the computer readable program instructions byutilizing state information of the computer readable programinstructions to personalize the electronic circuitry, in order toperform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions. These computer readable programinstructions can be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create method for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks. These computer readable program instructions can also be storedin a computer readable storage medium that can direct a computer, aprogrammable data processing apparatus, and/or other devices to functionin a particular manner, such that the computer readable storage mediumhaving instructions stored therein comprises an article of manufactureincluding instructions which implement aspects of the function/actspecified in the flowchart and/or block diagram block or blocks. Thecomputer readable program instructions can also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational acts to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams can represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks can occur out of theorder noted in the Figures. For example, two blocks shown in successioncan, in fact, be executed substantially concurrently, or the blocks cansometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While the subject matter has been described above in the general contextof computer-executable instructions of a computer program product thatruns on a computer and/or computers, those skilled in the art willrecognize that this disclosure also can be implemented in combinationwith other program modules. Generally, program modules include routines,programs, components, data structures, etc. that perform particulartasks and/or implement particular abstract data types. Moreover, thoseskilled in the art will appreciate that the inventivecomputer-implemented methods can be practiced with other computer systemconfigurations, including single-processor or multiprocessor computersystems, mini-computing devices, mainframe computers, as well ascomputers, hand-held computing devices (e.g., PDA, phone),microprocessor-based or programmable consumer or industrial electronics,and the like. The illustrated aspects can also be practiced indistributed computing environments where tasks are performed by remoteprocessing devices that are linked through a communications network.However, some, if not all aspects of this disclosure can be practiced onstand-alone computers. In a distributed computing environment, programmodules can be located in both local and remote memory storage devices.

As used in this application, the terms “component,” “system,”“platform,” “interface,” and the like, can refer to and/or can include acomputer-related entity or an entity related to an operational machinewith one or more specific functionalities. The entities disclosed hereincan be either hardware, a combination of hardware and software,software, or software in execution. For example, a component can be, butis not limited to being, a process running on a processor, a processor,an object, an executable, a thread of execution, a program, and/or acomputer. By way of illustration, both an application running on aserver and the server can be a component. One or more components canreside within a process and/or thread of execution and a component canbe localized on one computer and/or distributed between two or morecomputers. In another example, respective components can execute fromvarious computer readable media having various data structures storedthereon. The components can communicate via local and/or remoteprocesses such as in accordance with a signal having one or more datapackets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across a networksuch as the Internet with other systems via the signal). As anotherexample, a component can be an apparatus with specific functionalityprovided by mechanical parts operated by electric or electroniccircuitry, which is operated by a software or firmware applicationexecuted by a processor. In such a case, the processor can be internalor external to the apparatus and can execute at least a part of thesoftware or firmware application. As yet another example, a componentcan be an apparatus that provides specific functionality throughelectronic components without mechanical parts, wherein the electroniccomponents can include a processor or other method to execute softwareor firmware that confers at least in part the functionality of theelectronic components. In an aspect, a component can emulate anelectronic component via a virtual machine, e.g., within a cloudcomputing system.

In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. Moreover, articles “a” and “an” as used in thesubject specification and annexed drawings should generally be construedto mean “one or more” unless specified otherwise or clear from contextto be directed to a singular form. As used herein, the terms “example”and/or “exemplary” are utilized to mean serving as an example, instance,or illustration. For the avoidance of doubt, the subject matterdisclosed herein is not limited by such examples. In addition, anyaspect or design described herein as an “example” and/or “exemplary” isnot necessarily to be construed as preferred or advantageous over otheraspects or designs, nor is it meant to preclude equivalent exemplarystructures and techniques known to those of ordinary skill in the art.

As it is employed in the subject specification, the term “processor” canrefer to substantially any computing processing unit or devicecomprising, but not limited to, single-core processors;single-processors with software multithread execution capability;multi-core processors; multi-core processors with software multithreadexecution capability; multi-core processors with hardware multithreadtechnology; parallel platforms; and parallel platforms with distributedshared memory. Additionally, a processor can refer to an integratedcircuit, an application specific integrated circuit (ASIC), a digitalsignal processor (DSP), a field programmable gate array (FPGA), aprogrammable logic controller (PLC), a complex programmable logic device(CPLD), a discrete gate or transistor logic, discrete hardwarecomponents, or any combination thereof designed to perform the functionsdescribed herein. Further, processors can exploit nano-scalearchitectures such as, but not limited to, molecular and quantum-dotbased transistors, switches and gates, in order to optimize space usageor enhance performance of user equipment. A processor can also beimplemented as a combination of computing processing units. In thisdisclosure, terms such as “store,” “storage,” “data store,” datastorage,” “database,” and substantially any other information storagecomponent relevant to operation and functionality of a component areutilized to refer to “memory components,” entities embodied in a“memory,” or components comprising a memory. It is to be appreciatedthat memory and/or memory components described herein can be eithervolatile memory or nonvolatile memory, or can include both volatile andnonvolatile memory. By way of illustration, and not limitation,nonvolatile memory can include read only memory (ROM), programmable ROM(PROM), electrically programmable ROM (EPROM), electrically erasable ROM(EEPROM), flash memory, or nonvolatile random access memory (RAM) (e.g.,ferroelectric RAM (FeRAM). Volatile memory can include RAM, which canact as external cache memory, for example. By way of illustration andnot limitation, RAM is available in many forms such as synchronous RAM(SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rateSDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM),direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), andRambus dynamic RAM (RDRAM). Additionally, the disclosed memorycomponents of systems or computer-implemented methods herein areintended to include, without being limited to including, these and anyother suitable types of memory.

What has been described above include mere examples of systems andcomputer-implemented methods. It is, of course, not possible to describeevery conceivable combination of components or computer-implementedmethods for purposes of describing this disclosure, but one of ordinaryskill in the art can recognize that many further combinations andpermutations of this disclosure are possible. Furthermore, to the extentthat the terms “includes,” “has,” “possesses,” and the like are used inthe detailed description, claims, appendices and drawings such terms areintended to be inclusive in a manner similar to the term “comprising” as“comprising” is interpreted when employed as a transitional word in aclaim. The descriptions of the various embodiments have been presentedfor purposes of illustration, but are not intended to be exhaustive orlimited to the embodiments disclosed. Many modifications and variationswill be apparent to those of ordinary skill in the art without departingfrom the scope and spirit of the described embodiments. The terminologyused herein was chosen to best explain the principles of theembodiments, the practical application or technical improvement overtechnologies found in the marketplace, or to enable others of ordinaryskill in the art to understand the embodiments disclosed herein.

What is claimed is:
 1. A superconducting device, comprising: a first surface acoustic wave resonator comprising a first low-loss piezo-electric dielectric substrate; a second surface acoustic wave resonator comprising a second low-loss piezo-electric dielectric substrate; a Josephson ring modulator coupled to the first surface acoustic wave resonator and the second surface acoustic wave resonator, wherein the Josephson ring modulator is a dispersive nonlinear three-wave mixing element; a first interdigitated capacitance device positioned at a first center of the first surface acoustic wave resonator, wherein a first set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the first interdigitated capacitance device; and a second interdigitated capacitance device positioned at a second center of the second surface acoustic wave resonator, wherein a second set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the second interdigitated capacitance device.
 2. The superconducting device of claim 1, wherein the first surface acoustic wave resonator comprises a first superconducting Bragg mirror and a second superconducting Bragg mirror separated from the first superconducting Bragg mirror by a first distance, and wherein the second surface acoustic wave resonator comprises a third superconducting Bragg mirror and a fourth superconducting Bragg mirror separated from the third superconducting Bragg mirror by a second distance, and wherein the first distance and the second distance are odd integer multiples of a half-wavelength supported by the first surface acoustic wave resonator and the second surface acoustic wave resonator.
 3. The superconducting device of claim 1, wherein the first surface acoustic wave resonator is spatially and spectrally separated from the second surface acoustic wave resonator.
 4. The superconducting device of claim 1, further comprising: a first coupling capacitor connected via a first superconducting wire to a first port of a pump; and a second coupling capacitor connected via a second superconducting wire to a second port of the pump, wherein the first superconducting wire and the second superconducting wire are phase matched.
 5. The superconducting device of claim 1, further comprising: a first external feedline coupled to the first surface acoustic wave resonator through a first interdigitated capacitance device, wherein the first external feedline carries first input signals and first output signals of the first surface acoustic wave resonator; and a second external feedline coupled to the second surface acoustic wave resonator through a second interdigitated capacitance device, wherein the second external feedline carries second input signals and second output signals of the second surface acoustic wave resonator.
 6. The superconducting device of claim 1, further comprising: one or more external superconducting magnetic coils, wherein magnetic flux threading the Josephson ring modulator is induced through the one or more external superconducting magnetic coils.
 7. The superconducting device of claim 1, wherein the first low-loss piezo-electric dielectric substrate and the second low-loss piezo-electric dielectric substrate comprise a material selected from a group of materials consisting of quartz, gallium arsenide, lithium niobite, and zinc oxide.
 8. A superconducting circuit, comprising: a Josephson ring modulator; a first surface acoustic wave resonator coupled via a first superconducting wire to a first node of the Josephson ring modulator and via a second superconducting wire to a second node of the Josephson ring modulator, wherein the first superconducting wire and the second superconducting wire comprise a same length; and a second surface acoustic wave resonator coupled via a third superconducting wire to a third node of the Josephson ring modulator and via a fourth superconducting wire to a fourth node of the Josephson ring modulator, wherein the third superconducting wire and the fourth superconducting wire comprise a same length, and wherein the first surface acoustic wave resonator is spatially and spectrally separated from the second surface acoustic wave resonator.
 9. The superconducting circuit of claim 8, wherein the first surface acoustic wave resonator comprises a first superconducting Bragg mirror and a second superconducting Bragg mirror separated from the first superconducting Bragg mirror by a first distance, and wherein the second surface acoustic wave resonator comprises a third superconducting Bragg mirror and a fourth superconducting Bragg mirror separated from the third superconducting Bragg mirror by a second distance, and wherein the first distance and the second distance are odd integer multiples of a half-wavelength supported by the first surface acoustic wave resonator and the second surface acoustic wave resonator.
 10. The superconducting circuit of claim 8, further comprising: a first interdigitated capacitance device positioned at a first center of the first surface acoustic wave resonator, wherein a first set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the first interdigitated capacitance device; and a second interdigitated capacitance device positioned at a second center of the second surface acoustic wave resonator, wherein a second set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the second interdigitated capacitance device.
 11. The superconducting circuit of claim 8, further comprising: a first external feedline coupled to the first surface acoustic wave resonator through a first interdigitated capacitance device, wherein the first external feedline carries first input signals and first output signals of the first surface acoustic wave resonator; and a second external feedline coupled to the second surface acoustic wave resonator through a second interdigitated capacitance device, wherein the second external feedline carries second input signals and second output signals of the second surface acoustic wave resonator.
 12. The superconducting circuit of claim 8, further comprising: a pump port coupled to the Josephson ring modulator, wherein a pump drive is injected to the Josephson ring modulator through the pump port.
 13. The superconducting circuit of claim 8, wherein the Josephson ring modulator is a dispersive nonlinear three-wave mixing element.
 14. A method, comprising: coupling a first superconducting surface acoustic wave resonator to a Josephson ring modulator; coupling a second superconducting surface acoustic wave resonator to the Josephson ring modulator, wherein the Josephson ring modulator comprises one or more Josephson junctions arranged in a Wheatstone-bridge configuration, and wherein the Josephson ring modulator is a dispersive nonlinear three-wave mixing element; positioning a first interdigitated capacitance device at a first center of the first superconducting surface acoustic wave resonator, wherein a first set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the first interdigitated capacitance device; and positioning a second interdigitated capacitance device at a second center of the second superconducting surface acoustic wave resonator, wherein a second set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the second interdigitated capacitance device.
 15. The method of claim 14, further comprising: forming the first superconducting surface acoustic wave resonator comprising separating a first superconducting Bragg mirror from a second superconducting Bragg mirror by a first distance; and forming the second superconducting surface acoustic wave resonator comprising separating a third superconducting Bragg mirror from a fourth superconducting Bragg mirror by a second distance, and wherein the first distance and the second distance are odd integer multiples of a half-wavelength supported by the first superconducting surface acoustic wave resonator and the second superconducting surface acoustic wave resonator.
 16. The method of claim 14, further comprising: coupling a first external feedline to the first superconducting surface acoustic wave resonator through a first interdigitated capacitance device, wherein the first external feedline carries first input signals and first output signals of the first superconducting surface acoustic wave resonator; and coupling a second external feedline to the second superconducting surface acoustic wave resonator through a second interdigitated capacitance device, wherein the second external feedline carries second input signals and second output signals of the second superconducting surface acoustic wave resonator.
 17. A superconducting device, comprising: a first superconducting surface acoustic wave resonator comprising a first interdigitated capacitance device positioned at a first center of the first superconducting surface acoustic wave resonator, a first superconducting Bragg mirror and a second superconducting Bragg mirror separated from the first superconducting Bragg mirror by a first distance; a second superconducting surface acoustic wave resonator comprising a second interdigitated capacitance device positioned at a second center of the second superconducting surface acoustic wave resonator comprises a third superconducting Bragg mirror and a fourth superconducting Bragg mirror separated from the third superconducting Bragg mirror by a second distance, wherein the first distance and the second distance are odd integer multiples of a half-wavelength supported by the first superconducting surface acoustic wave resonator and the second superconducting surface acoustic wave resonator; and a Josephson ring modulator coupled to the first superconducting surface acoustic wave resonator and the second superconducting surface acoustic wave resonator, wherein a first set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the first interdigitated capacitance device, and wherein a second set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the second interdigitated capacitance device.
 18. The superconducting device of claim 17, further comprising: a first coupling capacitor connected to a first port of a pump via a first superconducting wire comprising a first wire length; and a second coupling capacitor connected to a second port of the pump via a second superconducting wire comprising a second wire length, wherein the first wire length and the second wire length are a same wire length.
 19. The superconducting device of claim 17, wherein the first interdigitated capacitance device is connected to a first external port via a first superconducting wire and the second interdigitated capacitance device is connected to a second external port via a second superconducting wire, wherein first input signals and first output signals of the first superconducting surface acoustic wave resonator are carried over the first superconducting wire and second input signals and second output signals of the second superconducting surface acoustic wave resonator are carried over the second superconducting wire.
 20. A superconducting device, comprising: a first superconducting surface acoustic wave resonator comprising a first superconducting Bragg mirror and a second superconducting Bragg mirror separated from the first superconducting Bragg mirror by a first distance; a second superconducting surface acoustic wave resonator comprising a third superconducting Bragg mirror and a fourth superconducting Bragg mirror separated from the third superconducting Bragg mirror by a second distance, wherein the first distance and the second distance are odd integer multiples of a half-wavelength supported by the first superconducting surface acoustic wave resonator and the second superconducting surface acoustic wave resonator, and wherein the second superconducting surface acoustic wave resonator is spatially and spectrally separated from the first superconducting surface acoustic wave resonator; and a Josephson ring modulator comprising a first set of opposite nodes and a second set of opposite nodes, the Josephson ring modulator is connected to the first superconducting surface acoustic wave resonator via the first set of opposite nodes and to the second superconducting surface acoustic wave resonator via the second set of opposite nodes.
 21. The superconducting device of claim 20, further comprising: a first interdigitated capacitance device positioned at a first center of the first superconducting surface acoustic wave resonator, wherein the first interdigitated capacitance device couples between the Josephson ring modulator and the first superconducting surface acoustic wave resonator; and a second interdigitated capacitance device positioned at a second center of the second superconducting surface acoustic wave resonator, wherein the second interdigitated capacitance device couples between the Josephson ring modulator and the second superconducting surface acoustic wave resonator.
 22. The superconducting device of claim 20, wherein the Josephson ring modulator is a dispersive nonlinear three-wave mixing element.
 23. The superconducting device of claim 17, wherein the Josephson ring modulator is a dispersive nonlinear three-wave mixing element.
 24. The superconducting device of claim 1, further comprising: a pump port coupled to the Josephson ring modulator, wherein a pump drive is injected to the Josephson ring modulator through the pump port.
 25. The method of claim 14, further comprising: connecting a first coupling capacitor coupled to the Josephson ring modulator to a first port of a pump via a first superconducting wire; and connecting a second coupling capacitor of the Josephson ring modulator to a second port of the pump via a second superconducting wire, wherein the first superconducting wire and the second superconducting wire are phase matched. 